Griffin sustained a Grade 1 sprain of the lateral collateral ligament after being hit by Baltimore Ravens tackle Haloti Ngata during the Redskins' 31-28 overtime victory on Sunday.
"He's definitely not ruled out for the Cleveland game," said Shanahan, whose team have won four straight and are second place in the NFC East, one game behind the New York Giants.
"There are different grades - 1, 2 and 3," he told reporters. "It's a Grade 1, so that was a good sign. We did not know going into it if it was a Grade 1, 2 or 3.
"It's a Grade 1 and he's got some mild swelling. You're hoping with rehab it gets better very quickly - but we don't know for sure.
"We'll have to go day-by-day and evaluate it day-by-day."
Griffin has been sensational this season, throwing for 18 touchdowns while running for six more.
Rookie Kirk Cousins replaced Griffin against Baltimore and rallied the Redskins to the victory.
Shanahan defended Griffin's decision to run the ball with less than two minutes to play against the Ravens, who were leading 28-20 at the time.
Griffin, popularly known as 'RG3', ran for 13 yards before getting whacked by Ngata.
"To me, you've got the final drive in the fourth quarter," said Shanahan. "He's trying to make a play and I'd say what Robert was trying to do is score a touchdown, what competitors would do.
"It's like a playoff game to us because we knew we had to win and Robert was going to do anything he could to get the first down.
"In normal circumstances, he probably would've slid or took off to the outside, but in that situation he's trying to do whatever he could to make a play." (Reporting By Steve Ginsburg; Editing by Peter Rutherford)
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- American Football
- Baltimore Ravens
- Haloti Ngata